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 Subject: mathematical formula Category: Science > Math Asked by: radom-ga List Price: \$10.00 Posted: 02 Oct 2002 01:19 PDT Expires: 01 Nov 2002 00:19 PST Question ID: 71521
 ```what is a formula that calculates the number of possible combinations of three members from n numbers, where n is a real number.```
 Subject: Re: mathematical formula Answered By: johnny_phoenix-ga on 02 Oct 2002 02:31 PDT
 ```the general formula is n! n_C_k = ---------- k!(n - k)! where n is a real number and k is the number selected (in your case 3) "3!" is for example 3x2x1 "n!" would be n x(n-1)x(n-2)and so on until n reaches 1. so your finished formula would be n! n_C_3 = ---------- 3!(n - 3)! For more explantion and examples on how this works, check out Ask Doctor Math http://mathforum.org/dr.math/faq/faq.comb.perm.html This is a very easy to understand page that will help you understand how the formula works. Example ******* suppose we want to find out the number of ways we can arrange 1 2 3. you can write them all out and know it reaches 6 or you can use the formula 3_n_3 = 3! ---------- 3! (3-3)! = 3x2x1 ----------- 3x2x1 x(0) = 6 --- 0 = 6 I hope this helps. Johnny Phoenix``` Clarification of Answer by johnny_phoenix-ga on 02 Oct 2002 07:17 PDT ```oops, well spotted "0!" = 1 not 0, apologies. lol @ asterisk man...good questions indeed, not sure we're allowed to answer them for free though lol.```
 ```A small typo, it is (3-3)!, which is (0)! which equas 1. This means the result from this formula is 1 rahter than 6. An thats correct as the combination formula ignores the order of the items being combined. So '123' is considerd the same as '321'. If you want to count the different orderings then you want the permutation formula which is n! n_P_k = -------- (n - k)! Which in you case would give the answer of 6. Cheers Chris```
 ```Not to be picky but isnt n! usually only defined for non-negative integers? The question asked for n to be a real number. Most likely the question asker did not intend to select 3 items out of a real number. what does 24.5421 choose 3 mean anyway? what is 24.5421! ? (windows calculator says 24.5421! = 3534876327450063425731321.6696764 but dont ask me where they come up with that) Anyway, I'll still agree with the answer other than the "real" part (and that x/0=x part (o: ). If someone can point out the answers to the two questions I've posed I'd be interested in them...though not enough to make it a question of my own (o:```
 ```search for Gamma function . Eg. http://mathforum.org/library/drmath/view/54540.html . HTH & Bye, \/#_|{>/```